The traditional low rank representation model is of low accuracy, when it is applied to high dimensional data clustering. Therefore, a kind of Laplacian regularized hyperbolic tangent function low-rank subspace clustering(LRHT-LRSC) algorithm is proposed. The LRHT-LRSC algorithm can compact approximation to the rank by using the hyperbolic tangent function instead of nuclear norm, and the accuracy of data clustering can be improved by using the Laplacian regularizer describing the instrinsic geometrical structures of the data. Then, the coefficient matrix and the similarity matrix of the data samples are constructed. Finally, the final clustering results are obtained by using the spectral clustering method. Experimental results on synthetic data sets, real data Extended Yale B and Hopkins 155 show that the proposed algorithm improves the accuracy and robustness of clustering.